At the climax of Harry Potter and the Chamber of Secrets, Harry pulls (unnecessary spoiler alert) the Sword of Godric Gryffindor out of the Sorting Hat, and uses it to great effect against the Heir of Slytherin and his pet monstrosity. Like King Arthur before him, Harry draws a sword out of an unlikely place (get your mind out of the gutter!) and fulfills his heroic destiny; all's well and good.
"All hail Harry, King of the Britons!"
But it's never established whether any of the other Four Founders have weapons of their own hidden in the depths of the Sorting Hat. They've all got items which are important to them (the Diadem of Ravenclaw, the Cup of Helga Hufflepuff, Slytherin's Locket), but these last three are merely powerful objects, not weapons they might hand down through the fog of ages to help their future students in their hour of need.
Personally, I like to think that there are weapons for each Founder, and for the amusement of my readers I will now take a moment to do some baseless conjecture on the subject.
The Dagger of Salazar Slytherin
Figuring out Slytherin's weapon was almost too easy. It's obvious, really. For a House that's willing to "use any means / To achieve their ends", a dagger is really the only option. Naturally, it would be a poisoned dagger. Possibly made of a basilisk fang, or at the very least imbued with the beast's venom.
The Shield of Helga Hufflepuff
At first, a club or mace seemed like the obvious choice. They're heavy, blunt, and associated with wood and stone, respectively. A morningstar (a spiked mace, usually round-headed) would even mimic the shape of the Earth, which is Hufflepuff's element.
But then I thought "perhaps not": Hufflepuff is defensive, not offensive. If the fight comes to them, they will meet it head-on, but they don't seek out battle. So a shield makes the most sense for the heirs of Hufflepuff. (And before you ask, no, I'm not sticking Hufflepuffs with the "lame weapon". Anyone who's familiar with Captain America knows that a shield bash can do some serious damage in the right hands.)
The Bow of Rowena Ravenclaw
Ravenclaw has her intelligence-boosting Diadem, which Hermione will tell you is a weapon in its' own right. But being wise, Rowena Ravenclaw no doubt realized that increased intelligence doesn't mean anything if it can't keep you alive long enough to use it. And surely she would realize that sometimes an application of force, in just the right place, is the wisest course of action.
With this in mind, a bow (and arrows, most likely bronze-tipped) would make the most sense as the signature weapon of House Ravenclaw. A bow allows the wielder to observe any conflict from a distance, carefully select the foe who poses the greatest threat, and fell them before they get close enough to do damage to one's self or allies.
Discuss: Do you disagree with any of these choices? What do you think the Founders' weapons would be?